#)Giải :

\(\left(1+2+3+...+50\right)x=2550\)

Xét tổng trong ngoặc :

Tổng này có ( 50 - 1 ) : 1 + 1 = 50 số hạng

Tổng này bằng ( 50 + 1 ) x 50 : 2 = 1275 

\(\Rightarrow1275\times x=2550\)

\(\Rightarrow x=2\)

\(\frac{\left(50+1\right)\times50}{2}\times x=2550\)

\(1275\times x=2550\)

\(x=2\)

\(\left(1+2+3+...+50\right)\times x=2550\)

\(\Rightarrow\frac{\left(50+1\right)50}{2}\times x=2550\)

\(\Rightarrow1275\times x=2550\)

\(\Rightarrow x=2550\div1275=2\)

Vây \(x=2\)

\(x+2x+3x+4x=100\)

\(x\left(1+2+3+4\right)=100\)

\(x\times10=100\)

\(x=100\div10\)

\(x=10\)

x*(1+2+3+4) = 100

x*10 = 100

x = 10

x + 2*x + 3*x + 4*x = 100

x * ( 2 + 3 + 4 + 1) = 100

x * 10 = 100

x        = 100 : 10

x         = 10

Đặt \(x-3=t\) thì pt đã cho trở thành :

\(\frac{3}{t}-\frac{2}{t+2}=\frac{t+2}{2}-\frac{t}{3}\)

\(\Leftrightarrow\frac{3t+6-2t}{t\left(t+2\right)}=\frac{3t+6-2t}{6}\)

\(\Leftrightarrow\left(t+6\right)\left[\frac{1}{t\left(t+2\right)}-\frac{1}{6}\right]=0\)

\(\Leftrightarrow\left[{}\begin{matrix}t+6=0\\\frac{1}{t\left(t+2\right)}=\frac{1}{6}\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}t=-6\\t^2+2t-6=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x-3=-6\\\left(t+1\right)^2=7\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-3\\t=\sqrt{7}-1\\t=-\sqrt{7}-1\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=2+\sqrt{7}\\x=2-\sqrt{7}\end{matrix}\right.\) ( TM )

Ta có: A = (x + 2)(x - 3) + x(x - 1) - 4 = x² - 3x + 2x - 6 + x² - x - 4 = 2x² - 2x - 10 = 2(x² - x + 1/4) - 21/2 = 2(x - 1/2)² - 21/2

Ta luôn có: 2(x - 1/2)² \(\ge\)0 \(\forall\)x

=> 2(x - 1/2)² - 21/2 \(\ge\)-21/2 \(\forall\)x

hay A \(\ge\)-21/2 \(\forall\)x

Dấu "=" xảy ra <=> x -1/2 = 0 <=> x = 1/2

vậy Min của A = -21/2 tại x = 1/2

\(A=\left(x+2\right)\left(x-3\right)+x\left(x-1\right)-4\)

\(\Leftrightarrow A=x^2-x-6+x^2-x-4\)

\(\Leftrightarrow A=2x^2-2x-10\)

\(\Leftrightarrow A=2\left(x^2-x-5\right)\)

\(\Leftrightarrow A=2\left(x^2-2.\frac{1}{2}x+\frac{1}{4}-\frac{21}{4}\right)\)

\(\Leftrightarrow A=2\left[\left(x-\frac{1}{2}\right)^2-\frac{21}{4}\right]\)

\(\Leftrightarrow A=2\left[\left(x-\frac{1}{2}\right)^2\right]-\frac{42}{4}\ge-\frac{42}{4}\)

Vậy \(A_{min}=\frac{-42}{4}\Leftrightarrow x=\frac{1}{2}\)

1.

a, (x+50)*2=220

=> 2x+100=220

=> 2x = 120

=> x= 60

b, (2x-75)*12=144

=> 24x-900=144

=> 24x=1044

=>  x= 43,5

c, (47-3x)=5

=> 47-3x=5

=> 3x=42

=> x= 14

A. ( x + 50 ) x 2= 220

=> 2x + 100 = 220

=> 2x = 220 - 100

=> 2x = 120

=> x = 120 : 2

=> x = 60

B. ( 2x - 75 ) x 12 = 144

=> (2x - 75) x 12 = 144

=> 2x - 75 = 144 : 12

=> 2x - 75 = 12

=> 2x = 75 + 12 

=> 2x = 87

=> x = 87 : 2 = 43,5

C. 47 - 3x = 5

=> 3x = 47 - 5 = 42

=> x = 42 : 3

=> x = 14.

2)1 + 2 + 3 + 4 + 5 +..+ X = 2550

=> \(\frac{x.\left(x+1\right)}{2}\)=2550

=> x.(x+1) = 2550 x 2 = 5100. Mà không có 2 số liên tiếp nào nhân với nhau bằng 5100 nên x không thỏa mãn đề bài.

3)Đề sai nha bạn.

a)\(\left(x+50\right).2=220\)

\(\left(x+50\right)=220:2\)

\(x+50=110\)

\(x=110-50\)

\(x=60\)

b)\(\left(2x-75\right).12=144\)

\(\left(2x-75\right)=144:12\)

\(2x-75=12\)

\(2x=12+75\)

\(2x=87\)

\(x=87:2\)

\(x\notin N\)

c)\(\left(47-3x\right)=5\)

\(3x=47-5\)

\(3x=42\)

\(x=42:3\)

\(x=14\)

1170 : ( x - 13 ) = 339 - 3 * 100

1170 : ( x - 13 ) = 39

             x - 13   = 1170 : 39 

             x - 13    = 30

                     x    = 30 + 13 

                     x     = 43 .

10-(5-x)=30+(2x-3)

10-5+x=30+2x-3

5+x=27+2x

x-2x=27-5

-x=22

x=-22

Cảm ơn bạn Thùy Trang